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Correction of hydraulic radius

Because the correlation structure of the 3-D image produced by rand3d.f only approximates that of the input 2-D correlation function, a modification is utilized to directly match the surface area fraction (via the hydraulic radius) of the 3-D image to its 2-D counterpart, greatly improving the agreement between the 2-D and 3-D correlations [14]. Typically, the IMAGE3D.OUT microstructure file produced by rand3d.f is renamed and analyzed using the program stat3d.c. This C program (listing provided in Appendix B), will determine the phase volume fractions and surface area fractions for each phase present in the microstructure. The surface area fractions are reported on a gypsum-free basis, so the user must be sure that the 2-D image has also been analyzed on a gypsum-free basis (i.e., considering only the C₃S, C₂S, C₃A, and C₄AF). The needed surface area count for a phase can be determined by multiplying the total surface area count by the surface (perimeter) fraction determined in analyzing the 2-D SEM image. From this, the appropriate value of hydraulic radius, R_h, can be determined as:

  
Figure 4: Flowchart specifying filtering algorithm for assigning pixel phase values to the three-dimensional starting cement microstructure image.

This hydraulic radius is input into the program sinter3d.c (listing provided in Appendix B) which interchanges pixels of two specific phases to obtain the specified hydraulic radius for the first phase. This code was originally developed to simulate the sintering of a ceramic powder by exchanging solid pixels of high curvature with porosity pixels of low curvature [15]. The program is menu driven and the user must first read in the microstructure previously output by execution of rand3d.f, using menu selection 4. After this, the sintering algorithm (menu selection 2) can be executed to adjust the hydraulic radius. For this algorithm, the following inputs are required:

• the two phase IDs between which to execute the sintering algorithm; the first phase indicates the one whose hydraulic radius will be increased,
• the number of pixels of each phase to exchange in each cycle of the sintering algorithm (default value=200),
• the calculated target hydraulic radius (equation 3), and
• the radius of the digitized sphere [15] to be used in assessing curvature (default value=3).

The sintering algorithm will be iteratively executed until the desired hydraulic radius is achieved or an equilibrium is reached. At this point, the user may elect to output the resulting microstructure to a file using menu selection 3. A file named sintmic.img will be created for this output. The user may then exit the program and rename this output file to retain it for future use.

Next: Three-dimensional Cement Hydration Up: Two-dimensional to Three-dimensional Previous: Filtering of random